Oven Prep & Vegetable Toss : Position an oven rack in the center and preheat to 400°F (200°C). In a large bowl, combine the halved potatoes, sliced bell peppers, and grape tomatoes. Drizzle with 2 tablespoons of the olive oil, then sprinkle with the sliced garlic, kosher salt, black pepper, and smoked paprika. Toss thoroughly until everything is evenly coated.
Initial Vegetable Roast : Spread the vegetable mixture in a single, even layer on the heavy-duty half-sheet pan. Transfer to the preheated oven and roast for 25 minutes, allowing the potatoes to begin softening and the peppers to become tender.
Prepare the Salmon : While the vegetables are roasting, prepare the salmon. Pat the fillets completely dry with a paper towel. Arrange them on a plate or small tray and drizzle with the remaining 1½ tablespoons of olive oil, using your fingers to coat all sides.
Combine & Final Bake : After 25 minutes, carefully remove the pan from the oven. Gently move the vegetables to create spaces for the salmon fillets. Place the seasoned salmon on the pan among the vegetables. Return the pan to the oven and bake for another 12 to 15 minutes.
Check for Doneness : The meal is ready when the potatoes are fork-tender and the salmon is opaque and flakes easily with a fork. For precision, the internal temperature of the salmon should register 140°F (60°C) in the thickest part.
Stage 6: Finish with Freshness : Remove the sheet pan from the oven. Zest one of the lemons directly over the entire pan. In a small bowl, combine the chopped fresh parsley, mint, dill, and Kalamata olives. Sprinkle this vibrant mixture evenly over the salmon and vegetables. Finally, cut both lemons in half and squeeze the juice from two halves over the dish. Serve immediately with the remaining lemon wedges on the side.